# Sublimation temperature of water in vacuum = 150K ?

## Main Question or Discussion Point

I am trying to find references for the the Wikipedia article
Frost line (astrophysics)
I am having a hard time finding a reference for the "Sublimation temperature of water in vacuum" that is used for calculation of the current snow line. E.g.: I have found 150K in several places, without any reference.
I understand that it is not a single point but a function of time, and probably 150K was chosen because it takes a long time (how long?) for X% of ice to sublime.

Please try to give some hard reference (or calculation).

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SteamKing
Staff Emeritus
Homework Helper
I am trying to find references for the the Wikipedia article
Frost line (astrophysics)
I am having a hard time finding a reference for the "Sublimation temperature of water in vacuum" that is used for calculation of the current snow line. E.g.: I have found 150K in several places, without any reference.
I understand that it is not a single point but a function of time, and probably 150K was chosen because it takes a long time (how long?) for X% of ice to sublime.

Please try to give some hard reference (or calculation).

The reference for the calculation of the snow line in the wiki article is given quite clearly:

http://arxiv.org/abs/1207.4284

Now, you may have to search secondary sources from the article at this link to obtain the full details of the calculation.

A quick skim of the article seems to indicate that some rather complex phenomena are at work, and it is not at all clear that the temperature of 150 K is, in fact, the sublimation point for water in vacuo.

Well... the latest details in this wiki article were written by me (at least this part and this reference were added by me), you can see it in the history.

So believe me, I have read the referenced article, the problem is that this article just says:
"The snow line occurs at a temperature, Tsnow, that is in the range of 145 K (Podolak & Zucker 2004) to 170 K (Hayashi 1981),"
I do not have access to this works (they are offline resources) so I can't understand how this numbers were calculated.
I would like to reference a clear source of how exactly this temperature was calculated.

As for what you say that it is not at all clear that 150K is sublimation temp in vacuum, this is exaclty what i am talking about! every resource gives different values: e.g. the Britannica article says it is 150K .
Every source throws numbers at me, without any calculation, this is really bad...

Regards,

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So believe me, I have read the referenced article, the problem is that this article just says:
"The snow line occurs at a temperature, Tsnow, that is in the range of 145 K (Podolak & Zucker 2004) to 170 K (Hayashi 1981),"
I do not have access to this works (they are offline resources) so I can't understand how this numbers were calculated.
I would like to reference a clear source of how exactly this temperature was calculated
I found this paper ( not sure if this is what you are looking for) on http://onlinelibrary.wiley.com/doi/10.1111/maps.2004.39.issue-11/issuetoc , you have to scroll down a bit until you find :
A note on the snow line in protostellar accretion disks (pages 1859–1868) by M. PODOLAK and S. ZUCKER ; then click on the PDF(592K).
Hope this helps.

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D H
Staff Emeritus
II am having a hard time finding a reference for the "Sublimation temperature of water in vacuum" that is used for calculation of the current snow line. E.g.: I have found 150K in several places, without any reference.
You are asking the wrong question. The sublimation temperature of any substance in vacuum is zero kelvin.

The planets did not form in vacuum. They formed in a protoplanetary disk, where pressure was low but was not zero. The right question then is what were the pressure and temperature at various points from the proto-sun when the solar system formed, and given that, where did water and other volatiles condense? That's a good question, and there is no uniformly agreed-upon answer. That's why you'll see a range of answers to this question.

Bystander
Homework Helper
Gold Member
probably 150K was chosen because it takes a long time (how long?) for X% of ice to sublime.
You can play around with the Langmuir equation for evaporation rates for an idea. Lowest T for vapor pressure of water I've got at hand is CRC handbook which doesn't go much below 170 K, if memory serves, but you should be able to "ballpark" a number from there to 150.

I found this paper ( not sure if this is what you are looking for) on http://onlinelibrary.wiley.com/doi/10.1111/maps.2004.39.issue-11/issuetoc , you have to scroll down a bit until you find :
A note on the snow line in protostellar accretion disks (pages 1859–1868) by M. PODOLAK and S. ZUCKER ; then click on the PDF(592K).
Hope this helps.
Thanks, JCMacaw! This is a very interesting paper, and a new resource website for me ;)
I have just finished reading it, and unfortunately in spite of all the calculations there the magic number "150 K" jumps out of the blue (without any calculation) just by saying:
"At temperatures above ~150 K evaporative cooling becomes important and quickly becomes the dominant cooling mechanism."
"At 3 AU, where both the grain and the gas temperatures are near 150 K"
and at another point it states:
"For all these cases, the snow line where the ice grains first become stable falls where the temperature of both the grains and the gas is 143 K"
"The dotted horizontal line indicates the temperature of 143 K. This is where the grains begin to be stable against evaporation"

Maybe this temperatures are somehow taken from the distance of 3 AU or sometimes 3.2 AU (later number looks more correct by the charts).

I think that 143K refers to 3.2AU and it is the more precise number, while the 150K is at 3 AU and it is just a nice round number, am I correct?
Is this the right place to ask such questions, or are they too detailed and belong to another forum?

I feel that this 0.2AU difference is an important distance since we are in the middle of the Asteroid Belt, and there are a lot of asteroids that are either in or out of this distance.
Of course I understand that this is still theoretical value, but at least it should match the real calculations of the paper...

You are asking the wrong question. The sublimation temperature of any substance in vacuum is zero kelvin.
Indeed it is, I should have probably asked: what is the sublimation temperature at which the mass loss of water ice is negligible (eg 10%) during X years (eg from the formation of Solar System) + provide formula that this could be calculated with different values.

The planets did not form in vacuum. They formed in a protoplanetary disk, where pressure was low but was not zero. The right question then is what were the pressure and temperature at various points from the proto-sun when the solar system formed, and given that, where did water and other volatiles condense? That's a good question, and there is no uniformly agreed-upon answer. That's why you'll see a range of answers to this question.
I perfectly understand that, that is why I do not just ask what is the temperature, I ask to see the explanation for each number and its calculation, so I could write something like this:
The 170 K value is only when the H2O/H2 ratio is on the order of the solar value (+reference)
The 150 K value is if the water vapor abundance is constrained by the vapor pressure at the ambient disk temperature. (+reference)
etc...
etc...

and if a number doesn't have clear explanation, it doesn't belong in to Wikipedia scientific articles.

Regards,

D H
Staff Emeritus
Thanks, JCMacaw! This is a very interesting paper, and a new resource website for me ;)
I have just finished reading it, and unfortunately in spite of all the calculations there the magic number "150 K" jumps out of the blue (without any calculation) just by saying:
"At temperatures above ~150 K evaporative cooling becomes important and quickly becomes the dominant cooling mechanism."
"At 3 AU, where both the grain and the gas temperatures are near 150 K"
That is not the snow line temperature. That's merely the temperature at which evaporative cooling dominates over other cooling mechanisms. This is just one of many results in that paper that result from the execution of a lot of complex computer code. That code itself? It's not in the paper; it hardly ever is. The page count limitations preclude it.

I perfectly understand that, that is why I do not just ask what is the temperature, I ask to see the explanation for each number and its calculation, so I could write something like this:
The 170 K value is only when the H2O/H2 ratio is on the order of the solar value (+reference)
The 150 K value is if the water vapor abundance is constrained by the vapor pressure at the ambient disk temperature. (+reference)
I think you are asking for too much. The reasons for the discrepancies are much deeper than what you are trying to write. You are not going to find a formula for the frost line temperature. There are hidden assumptions, hidden computer codes, hidden analyses. A journal paper would have to be hundreds of pages long to expose those hidden items.

People disagree on the specific value, and that's all there is to it.

The 170 K figure is still very widely used. The paper that is the source of the 170 K figure is from 1981, but it still receives a lot more citations than does this 2004 paper by Podolak and Zucker. Several recent papers simply cite the 145 K to 170 K range (with references) and then use the 170 K figure, claiming that the lower figure would not change the results by much.

My suggestion to fix that wikipedia article: Simply change the sentence "This condensation temperature depends on the volatile substance and the partial pressure of vapor in the protostar nebula, e.g.: temperature of water snow line ranges from 145K (Podolak & Zucker 2004) to 170K (Hayashi 1981)" to "This condensation temperature depends on the volatile substance and the partial pressure of vapor in the protostar nebula, e.g.: temperature of water snow line ranges from 145K [reference link to Podolak & Zucker 2004] to 170K [reference link to Hayashi 1981]".

http://ptps.oxfordjournals.org/content/70/35 [Broken]

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http://ptps.oxfordjournals.org/content/70/35 [Broken]
Thanks for the explanations and the link.
I have updated the wiki article, Frost line (astrophysics), and gave the link to Hayashi paper, but although everybody refers to it in regard to snow line, actually this paper talks about magnetic fields and not about the snow line, for his calculations he just need the condensation temperature of ice, so he wrote (p.38):
"The condensation temperature of ice is simply taken as 170K"
without any reference or explanation. It looks like either I am looking at the wrong paper or everybody references this work just because he wrote that line.
Very strange. Btw, I found two more papers that reference to Hayashi and this 170 K.

Anyway, now the only big problem is that the previous edition of the "Frost line" wiki article stated 5 AU as the snow line without any reference and I removed it since all papers that i found were talking about ~3 AU.
But I am not totally content with it because now I have a contradiction with the Ceres wiki article and its reference that says:
"Surface water ice is unstable at distances less than 5 AU from the Sun"
http://www.astronoo.com/en/articles/frost-line.html
http://physicsworld.com/cws/article/news/2013/jul/18/snow-line-of-neighbouring-star-comes-into-view

How can I resolve it?
There is no paper for 5 AU snow line...

Regards,

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I am trying to find references for the the Wikipedia article
Frost line (astrophysics)
I am having a hard time finding a reference for the "Sublimation temperature of water in vacuum" that is used for calculation of the current snow line. E.g.: I have found 150K in several places, without any reference.
I understand that it is not a single point but a function of time, and probably 150K was chosen because it takes a long time (how long?) for X% of ice to sublime.

Please try to give some hard reference (or calculation).

Like you, I found temperature ranges between 150°K and 170°K for the snow line, but no explanation for why those particular temperatures were used. I also found references to 5 AU as being the snow line for our solar system. It was explained to me that distance of 5 AU was only during the protoplanetary disk stage of our solar system, and now the snow line should be between 2.7 AU and 3 AU. Frankly, that does not make sense to me. The snow line should have been much closer to the protostar before the sun began hydrogen fusion than it is now.

According to the above reference the condensation temperature of H2O at 10-4 bar is 182°K. Using the Stefan-Boltzmann law, that would put the snow line at 2.346 AU.

Source:
Solar System Abundances & Condensation Temperatures of the Elements - Katharina Lodders, The Astrophysical Journal, 591:1220–1247, July 10, 2003 [PDF]

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According to the above reference the condensation temperature of H2O at 10-4 bar is 182°K. Using the Stefan-Boltzmann law, that would put the snow line at 2.346 AU.
Thanks a lot for this info, I somehow missed Lodders paper before.
Although it contradicts a bit some other references that i found (see wiki article), eg see reference (Podolak and Zucker, 2010)
143 K at 3.2 AU to 150 K at 3 AU

Like you, I found temperature ranges between 150°K and 170°K for the snow line, but no explanation for why those particular temperatures were used. I also found references to 5 AU as being the snow line for our solar system. It was explained to me that distance of 5 AU was only during the protoplanetary disk stage of our solar system, and now the snow line should be between 2.7 AU and 3 AU. Frankly, that does not make sense to me. The snow line should have been much closer to the protostar before the sun began hydrogen fusion than it is now
Actually it is the opposite,
3AU was the distance of snow line during FORMATION of solar system, because the solar nebula was opaque and blocked sun radiation.
5AU is the CURRENT distance of snow line below which water on the SURFACE can't be stable.
however there are lots of solar system bodies (like CERES) that are between 3AU and 5AU that are made of Water Ice, this is because they were formed during formation of solar system when snow line was @3AU, and after that the water ice was covered by layer of infalling dust that now protects them from direct sunlight.
Please see the wiki article, I have updated all the info there.

There is however still one thing that doesn't make sense to me:
Lets take current solar system that is perfectly transparent,
If the condensation temp of water is 182K which puts it at 2.3 AU
or even if the condensation temp is at 150K which puts it at 3AU (as by other references)

Why is the snow line currently at 5AU?

this is still beyond me...

Regards,

Thanks a lot for this info, I somehow missed Lodders paper before.
Although it contradicts a bit some other references that i found (see wiki article), eg see reference (Podolak and Zucker, 2010)
143 K at 3.2 AU to 150 K at 3 AU

Actually it is the opposite,
3AU was the distance of snow line during FORMATION of solar system, because the solar nebula was opaque and blocked sun radiation.
5AU is the CURRENT distance of snow line below which water on the SURFACE can't be stable.
however there are lots of solar system bodies (like CERES) that are between 3AU and 5AU that are made of Water Ice, this is because they were formed during formation of solar system when snow line was @3AU, and after that the water ice was covered by layer of infalling dust that now protects them from direct sunlight.
Please see the wiki article, I have updated all the info there.

There is however still one thing that doesn't make sense to me:
Lets take current solar system that is perfectly transparent,
If the condensation temp of water is 182K which puts it at 2.3 AU
or even if the condensation temp is at 150K which puts it at 3AU (as by other references)

Why is the snow line currently at 5AU?

this is still beyond me...

Regards,
Thanks for the clarification. You may also find this interesting:

Critical Core Mass for Enriched Envelopes: The Role of H2O Condensation - arXiv : 1502.01160v1 [PDF]

This paper also uses 150°K as a constant, stating that it "...reside always in the region where H2O is in solid phase (or in the solid vapor transition), the profiles follow the moist adiabat."

160.9° = 3 AU. 150°K = 3.5 AU. 126.7°K = 5 AU

If the condensation temperature of H2O is 182°K at 10-4 bar, then would not any surface water-ice simply sublimate away at colder temperatures?

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If the condensation temperature of H2O is 182°K at 10-4 bar, then would not any surface water-ice simply sublimate away at colder temperatures?
What do u mean?? it is the opposite: The colder it is the less sublimation happens. so 182K looks like too HOT.

What do u mean?? it is the opposite: The colder it is the less sublimation happens. so 182K looks like too HOT.
I am thinking of water's triple point of 611.657 ± 0.010 Pa at 273.16°K. When the atmospheric pressure is less than 6.12 × 10-3 bar and the temperature is colder than 273.16°K, water-ice will go from solid to vapor directly. Therefore, I presume that if water-ice is under 10-4 bar or less of atmospheric pressure and colder than 182°K, that it will also undergo sublimation.

In space (vacuum) because of low pressure it is always sublimation only. there is never liquid state.

In space (vacuum) because of low pressure it is always sublimation only. there is never liquid state.
I do not think I made myself clear. What I am saying is that in space (10-4 bar) if the temperature is above 182°K then any surface water-ice will not remain solid, but rather become vapor. It has to be colder than 182°K in space for water-ice to remain stable. That should put the snow line at 2.3 AU, not 5 AU.

It has to be colder than 182°K in space for water-ice to remain stable. That should put the snow line at 2.3 AU, not 5 AU.
Well, this is exactly the confusion, 182K or even if it is 150K (which is at 3AU),

but were does 5AU come from? not clear...

P.S.
Of course you must remember that sublimation happens ALWAYS even at the coldest temperature (except absolute zero), but at very slow rate,
so the rate of sublimation should be lower than the rate of reaccretion, and this is the temperature that is considered the sublimation point.

D H
Staff Emeritus
Thanks for the explanations and the link.
I have updated the wiki article, Frost line (astrophysics), ...
A minor nit: Your reference to the 2012 Martin & Livio paper is to the arxiv preprint. It should be to the MNRAS Letters article where it was published, with the arxiv link as a backup for those who don't have free access to the journal. Here's a reference, and a link:

Martin, R. G., & Livio, M. (2012). On the evolution of the snow line in protoplanetary discs. Monthly Notices of the Royal Astronomical Society: Letters, 425(1), L6-L9.
http://mnrasl.oxfordjournals.org/content/425/1/L6.short.

Major nit: You've picked an article that doesn't have very many citations, and of those, many are self-citations by Martin or Livio. What Martin & Livio did in their paper was to try to reconcile the fact that models of location of the snow line in a protoplanetary disk disagree with what we see. Whether the Martin & Livio model becomes accepted science, it's a bit too early to tell.

What the models say is that the snow line migrates inward as the protostar and protoplanetary disk evolve (more below), with many models having the snow line migrating inside 1 AU. What observation says is that could not have been the case. Lecar et al. (see citation below) noted this problem in 2006.

Lecar, M., Podolak, M., Sasselov, D., & Chiang, E. (2006). On the location of the snow line in a protoplanetary disk. The Astrophysical Journal, 640(2), 1115.
http://iopscience.iop.org/0004-637X/640/2/1115
Arxiv pre-print: http://arxiv.org/abs/astro-ph/0602217

An even bigger problem is that you want one number. There is no one number. As mentioned above, the location of the snow line in a protoplanetary disk moves inward and then outward as the protostar and the protoplanetary disk evolved over time.

A very young protostar is much more luminous than its zero age main sequence counterpart. A one solar mass protostar first evolves along the Hayashi track, where luminosity decreases but temperature remains more or less constant. The core of the shrinking protostar ceases to be convective at some point, leading to a transition from the Hayashi track to the Henyey track, where temperature increases and luminosity remains more or less constant. Meanwhile, the protoplanetary disk also is evolving. Opacity, density, turbulence, and degree of ionization all play a role, and they all change.

Making a model that is consistent with physics and that is consistent with the observed makeup of our solar system (and now with other developing star systems) is still a work in progress.

Anyway, now the only big problem is that the previous edition of the "Frost line" wiki article stated 5 AU as the snow line without any reference and I removed it since all papers that i found were talking about ~3 AU.
Why did you do that? Right now, it's much better (in my opinion) to say that people agree to disagree and cite a range of figures. One way to look at it is that it's somewhere inside 5.2 AU because of the observed stability of Jupiter's Trojan asteroids, somewhere outside 3 AU because by that point incoming comets are spouting water vapor.

Another way to look at it is that the concept of a snow line in vacuum is a bit nonsensical. The existence of a snow line in a protoplanetary disk makes sense because the pressure in a protoplanetary disk, while low, is not that of an extremely high vacuum.

The snow line should have been much closer to the protostar before the sun began hydrogen fusion than it is now.
You apparently are thinking that onset of fusion makes a protostar become more luminous. That isn't the case. What fusion does is the change the timescale of the evolution toward the protostar becoming a zero age main sequence star, where the star finally reaches equilibrium. You won't see a sudden change in luminosity as fusion begins. In fact, it's hard to pinpoint exactly when fusion does begin. It's not a quantum switch. The fusion rate instead gradually increases from near zero toward the quasi-stable value of a zero age main sequence star.

Well, this is exactly the confusion, 182K or even if it is 150K
The 182 K value arises from assuming a pressure of 10-4 bar. Most planetary scientists think the pressure was a bit lower than that, resulting in a somewhat lower figure. How much lower? Scientists agree to disagree. That's why you see a range of figures.

|Glitch|
An even bigger problem is that you want one number. There is no one number. As mentioned above, the location of the snow line in a protoplanetary disk moves inward and then outward as the protostar and the protoplanetary disk evolved over time.

A very young protostar is much more luminous than its zero age main sequence counterpart. A one solar mass protostar first evolves along the Hayashi track, where luminosity decreases but temperature remains more or less constant. The core of the shrinking protostar ceases to be convective at some point, leading to a transition from the Hayashi track to the Henyey track, where temperature increases and luminosity remains more or less constant. Meanwhile, the protoplanetary disk also is evolving. Opacity, density, turbulence, and degree of ionization all play a role, and they all change.

Making a model that is consistent with physics and that is consistent with the observed makeup of our solar system (and now with other developing star systems) is still a work in progress.
Clearly there is not going to be a single distance for the snow line as the sun evolves. As the sun's radius, surface temperature, and luminosity changes, so will the distance of the snow line.

You apparently are thinking that onset of fusion makes a protostar become more luminous. That isn't the case. What fusion does is the change the timescale of the evolution toward the protostar becoming a zero age main sequence star, where the star finally reaches equilibrium. You won't see a sudden change in luminosity as fusion begins. In fact, it's hard to pinpoint exactly when fusion does begin. It's not a quantum switch. The fusion rate instead gradually increases from near zero toward the quasi-stable value of a zero age main sequence star.
Thank you for the detailed explanation. And you were quite correct, I was considering the process more like a switch when a certain temperature was reached at the core. I had not considered that it would be a more gradual process.

The 182 K value arises from assuming a pressure of 10-4 bar. Most planetary scientists think the pressure was a bit lower than that, resulting in a somewhat lower figure. How much lower? Scientists agree to disagree. That's why you see a range of figures.
The range I most frequently encounter is between 170°K and 150°K, which puts the snow line range between 2.689 AU and 3.453 AU. The range I find for the atmospheric pressure of space is between 1 × 10−4 Pa to < 3 × 10−15 Pa. That is quite a range, and at least 5 orders of magnitude less pressure than 10-4 bar that gave us 182°K for the condensation of water-ice.